Abstract

By constructing a Lyapunov function, a new instability result is established,
which guarantees that the trivial solution of a certain nonlinear vector differential equation of
the fifth order is unstable. An example is also given to illustrate the importance of the result
obtained. By this way, our findings improve an instability result related to a scalar differential
equation in the literature to instability of the trivial solution to the afore-mentioned differential
equation.